Complex boundary conditions

[dynamic-queries]

Question❓

MWE:

using MethodOfLines, OrdinaryDiffEq, Plots, DomainSets, ModelingToolkit

@parameters t, x
@variables ψ(..)

Dt = Differential(t)
Dxx = Differential(x)^2

xmin = 0
xmax = 1
ϵ = 1e-2

V(x) = 0.0

eq = [(im*ϵ)*Dt(ψ(t,x)) ~ (-0.5*ϵ^2)Dxx(ψ(t,x)) + V(x)*ψ(t,x)] # You must enclose complex equations in a vector, even if there is only one equation

ψ0 = x -> exp((im/ϵ)*1e-1*sum(x))

bcs = [ψ(0,x) ~ ψ0(x),
    ψ(t,xmin) ~ exp((im/ϵ)*(1e-1*sum(xmin) - 0.5e-2*t)),
    ψ(t,xmax) ~ exp((im/ϵ)*(1e-1*sum(xmax) - 0.5e-2*t))]

domains = [t ∈ Interval(0, 1), x ∈ Interval(xmin, xmax)]

@named sys = PDESystem(eq, bcs, domains, [t, x], [ψ(t,x)])

disc = MOLFiniteDifference([x => 300], t)

prob = discretize(sys, disc)

sol = solve(prob, TRBDF2(), saveat = 0.01)

Use of complex valued boundary conditions, throws an assertion error. Is this a known issue ?

[ChrisRackauckas]

Yes it's not currently supported.